Originally Posted by
seerTneerGevoLI 1a.) Prove the sequence converges which is defined by x_1 = 3 and x_(n + 1) = 1/(4 - x_n)
b.) Now we know lim x_n exists... explain why lim x_(n + 1) must also exist, and further, explain why it must equal the same value.
c.) Of the recursive equation shown in a.), take the lim of each side of the recursive eq'n. to explicity compute lim x_n
My work:
a.) Now I am not exactly sure how to prove this... I've learned the epsilon method, showing that there exists one greater than 0.. blah blah blah. But I was thinking of maybe trying to use proof by induction to show:
0 <= x_n <= 3 and x_(n) is decreases, which will imply that {x_n} converges (by the monotone convergence thm)...